Finding Interesting Dynamics in the Asteroid Belt with Mathematica‘s AstronomicalData

Almost everyone has heard of the asteroid belt. This is the place between the orbit of Mars and Jupiter that is home to a very large percentage of the known minor planets in the solar system. Movies love to have space battles in asteroid belts to add to dramatic dogfight scenes. Even the Star Wars universe pays homage to asteroids: in The Empire Strikes Back, C3PO makes a popular statement about the possibility of successfully navigating an asteroid field.

Popular fiction, especially in Hollywood, loves to twist reality for cinematic effect. Often it shows an asteroid belt as an intricate maze of chaotically tumbling boulders that are moving at high speeds relative to each other, requiring advanced evasion techniques to avoid hitting one of them. They are also often shown to collide with each other at high speed, resulting in large explosions.

In reality, at least for our asteroid belt, things are not quite so dramatic. If you were actually in our asteroid belt, the chances that you would see an asteroid are fairly small. Most of them are quite small relative to the Earth and the space between them is relatively large. NASA has sent numerous probes through the belt, and not one has had an accidental encounter with an asteroid, although there have been a couple of intentional encounters. We know very little about the physical characteristics of asteroids compared to planets. Very few have been visited. However, their orbital dynamics are well studied and show some pretty amazing features. Let’s take a look at a view of all of the asteroids used in Mathematica‘s AstronomicalData out to the orbit of Jupiter.

This animation is great at showing the dynamic behavior of the asteroid belt, but I should point out a couple of obvious inaccuracies.

Size is not to scale, but distance is. All the planets are one size and all the asteroids are one size. They are rendered for visibility, not accurate appearance. This makes the asteroid belt look like an impenetrable wall. It’s far from that.

This animation is running far faster than real time. The entire animation runs over about a four-year time span with about a three-day time resolution between frames.

Still, the fluid motion is almost hypnotic to watch. In addition, a couple of things stand out. The outermost planet orbit shown is that of Jupiter. If you examine the animation closely, you will notice a couple of isolated “clouds” of asteroids orbiting along with Jupiter in its orbit, 60 degrees ahead of and behind the planet. These are well-known groups of asteroids called the “Greeks” and “Trojans”, respectively. They are trapped in the L4 and L5 points of the Jupiter-Sun system. Basically, these are a couple of gravity traps that in the case of the giant planet are deep enough to trap nearby asteroids. See the “Lagrange Points” Demonstration for more information on this topic. We can isolate the Greeks and Trojans in this animation for clarity.

If we look even more closely at the original animation, we see another clump on the opposite side of the asteroid belt from Jupiter. This clump is an isolated part of a group of asteroids known as the Hilda family. Most of this family of asteroids is buried in the main belt and so goes unnoticed. However, we can isolate just those asteroids and reveal an even more interesting dynamic arrangement. The Hilda family orbits the Sun three times for every two orbits of Jupiter. This 2:3 orbital resonance results in a group that appears to follow a triangular orbit.

In actuality every one of these is on a standard elliptical orbit, but their positions on those orbits maintain this triangular arrangement. Here is a notebook containing a single 3D frame from the animation, but with the orbits shown. Using your mouse with Mathematica or Mathematica Player, you can rotate the graphic to get a different perspective.

There are many other families of asteroids. Most don’t have such recognizable patterns, but there are at least a few patterns in all the perceived chaos. If you plot the semimajor axis versus the inclination of all the minor planets, many will fall into groups. These include spaces known as Kirkwood gaps and also clusters of asteroids that may indicate a collisional family (they may have been one object long ago, but have been broken up due to collisions).

The views above are just a small handful of the things you can encounter when analyzing large astronomy datasets. Can you find others?

Typically, asteroids are found observationally, either one at a time or as part of surveys of patches of the sky. Once the position is determined and it is tracked over some time period, its orbit can be determined. Only after many such orbit determinations are made can anyone even attempt to look for these patterns. Typically these patterns are found afterward.